Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with asymptotically periodic potentials

We consider one-dimensional Fokker-Planck and Schr\"odinger equations with a potential which approaches a periodic function at spatial infinity. We extend the low-energy expansion method, which was introduced in previous papers, to be applicable to such asymptotically periodic cases. Using this method, we study the low-energy behavior of the Green function.Comment: author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretica

A tight lower bound for an online hypercube packing problem and bounds for prices of anarchy of a related game

We prove a tight lower bound on the asymptotic performance ratio $\rho$ of the bounded space online $d$-hypercube bin packing problem, solving an open question raised in 2005. In the classic $d$-hypercube bin packing problem, we are given a sequence of $d$-dimensional hypercubes and we have an unlimited number of bins, each of which is a $d$-dimensional unit hypercube. The goal is to pack (orthogonally) the given hypercubes into the minimum possible number of bins, in such a way that no two hypercubes in the same bin overlap. The bounded space online $d$-hypercube bin packing problem is a variant of the $d$-hypercube bin packing problem, in which the hypercubes arrive online and each one must be packed in an open bin without the knowledge of the next hypercubes. Moreover, at each moment, only a constant number of open bins are allowed (whenever a new bin is used, it is considered open, and it remains so until it is considered closed, in which case, it is not allowed to accept new hypercubes). Epstein and van Stee [SIAM J. Comput. 35 (2005), no. 2, 431-448] showed that $\rho$ is $\Omega(\log d)$ and $O(d/\log d)$, and conjectured that it is $\Theta(\log d)$. We show that $\rho$ is in fact $\Theta(d/\log d)$. To obtain this result, we elaborate on some ideas presented by those authors, and go one step further showing how to obtain better (offline) packings of certain special instances for which one knows how many bins any bounded space algorithm has to use. Our main contribution establishes the existence of such packings, for large enough $d$, using probabilistic arguments. Such packings also lead to lower bounds for the prices of anarchy of the selfish $d$-hypercube bin packing game. We present a lower bound of $\Omega(d/\log d)$ for the pure price of anarchy of this game, and we also give a lower bound of $\Omega(\log d)$ for its strong price of anarchy

Mathematical Models and Exact Algorithms for the Colored Bin Packing Problem

This paper focuses on exact approaches for the Colored Bin Packing Problem (CBPP), a generalization of the classical one-dimensional Bin Packing Problem in which each item has, in addition to its length, a color, and no two items of the same color can appear consecutively in the same bin. To simplify modeling, we present a characterization of any feasible packing of this problem in a way that does not depend on its ordering. Furthermore, we present four exact algorithms for the CBPP. First, we propose a generalization of Val\'erio de Carvalho's arc flow formulation for the CBPP using a graph with multiple layers, each representing a color. Second, we present an improved arc flow formulation that uses a more compact graph and has the same linear relaxation bound as the first formulation. And finally, we design two exponential set-partition models based on reductions to a generalized vehicle routing problem, which are solved by a branch-cut-and-price algorithm through VRPSolver. To compare the proposed algorithms, a varied benchmark set with 574 instances of the CBPP is presented. Results show that the best model, our improved arc flow formulation, was able to solve over 62% of the proposed instances to optimality, the largest of which with 500 items and 37 colors. While being able to solve fewer instances in total, the set-partition models exceeded their arc flow counterparts in instances with a very small number of colors

Mechanism of atomic force microscopy imaging of three-dimensional hydration structures at a solid-liquid interface

Here we present both subnanometer imaging of three-dimensional (3D) hydration structures using atomic force microscopy (AFM) and molecular dynamics simulations of the calcite-water interface. In AFM, by scanning the 3D interfacial space in pure water and recording the force on the tip, a 3D force image can be produced, which can then be directly compared to the simulated 3D water density and forces on a model tip. Analyzing in depth the resemblance between experiment and simulation as a function of the tip-sample distance allowed us to clarify the contrast mechanism in the force images and the reason for their agreement with water density distributions. This work aims to form the theoretical basis for AFM imaging of hydration structures and enables its application to future studies on important interfacial processes at the molecular scale

Efeitos da temperatura de secagem do solo e extratores na solubilidade do manganês.

Temperatura de secagem do solo e das soluções extratoras EDTA, CuCl2 e MgCl2 na solubilidade do manganes

Zircon to monazite phase transition in CeVO4

X-ray diffraction and Raman-scattering measurements on cerium vanadate have been performed up to 12 and 16 GPa, respectively. Experiments reveal that at 5.3 GPa the onset of a pressure-induced irreversible phase transition from the zircon to the monazite structure. Beyond this pressure, diffraction peaks and Raman-active modes of the monazite phase are measured. The zircon to monazite transition in CeVO4 is distinctive among the other rare-earth orthovanadates. We also observed softening of external translational Eg and internal B2g bending modes. We attributed it to mechanical instabilities of zircon phase against the pressure-induced distortion. We additionally report lattice-dynamical and total-energy calculations which are in agreement with the experimental results. Finally, the effect of non-hydrostatic stresses on the structural sequence is studied and the equations of state of different phases are reported.Comment: 45 pages, 8 figures, 8 table

Magnetic and Metal-Insulator Transitions through Bandwidth Control in Two-Dimensional Hubbard Models with Nearest and Next-Nearest Neighbor Transfers

Numerical studies on Mott transitions caused by the control of the ratio between bandwidth and electron-electron interaction ($U$) are reported. By using the recently proposed path-integral renormalization group(PIRG) algorithm, physical properties near the transitions in the ground state of two-dimensional half-filled models with the nearest and the next-nearest neighbor transfers ($-t$ and $t'$, respectively) are studied as a prototype of geometrically frustrated system. The nature of the bandwidth-control transitions shows sharp contrast with that of the filling-control transitions: First, the metal-insulator and magnetic transitions are separated each other and the metal-insulator (MI) transition occurs at smaller $U$, although the both transition interactions $U$ increase with increasing $t'$. Both transitions do not contradict the first-order transitions for smaller $t'/t$ while the MI transitions become continuous type accompanied by emergence of {\it unusual metallic phase} near the transition for large $t'/t$. A nonmagnetic insulator phase is stabilized between MI and AF transitions. The region of the nonmagnetic insulator becomes wider with increasing $t'/t$. The phase diagram naturally connects two qualitatively different limits, namely the Hartree-Fock results at small $t'/t$ and speculations in the strong coupling Heisenberg limit.Comment: 30 pages including 20 figure

Effect of magnetic frustration on single-hole spectral function in the t-t'-t''-J model

We examine the effect of the magnetic frustration J' on the single-hole spectral function in the t-t'-t''-J model. At zero temperature, the exact diagonalization (ED) and the self-consistent Born approximation (SCBA) methods are used. We find that the frustration suppresses the quasiparticle (QP) weight at small momentum k, whereas the QP peak at k=(pi/2,pi/2) remains sharp. We also show the temperature dependence of the single-hole spectral function by using the ED method. It is found that the lineshapes at (pi/2,0) and (pi/2,pi/2) show different temperature dependence. These findings are consistent with the angle-resolved photoemission data on Sr2CuO2Cl2, and indicate the importance of the magnetic frustration on the electronic states of the insulating cuprates.Comment: 5 pages, 3 EPS figures, REVTeX, To be published in Phys. Rev. B, Vol. 59, Num. 3 (15 Jan. 1999